{"id":"max-sum-greedy-correctness","text":"The closed-form formula is equivalent to greedily picking all 1s, then all 0s, then -1s, which is provably optimal because item values are strictly ordered (1 > 0 > -1).","truth_value":"IN","source":"entries/2026/06/06/k-items-with-the-maximum-sum-solution.md","source_url":"","source_hash":"","justifications":[],"dependents":["greedy-algorithms-provably-optimal"],"metadata":{},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"max-sum-greedy-correctness","truth_value":"IN","reason":"premise"}]}}